Find all real numbers K such that the inequality $x^2 - 2(4K-1)x + 15K^2 - 2K- 7> 0$ holds for all real x.
+128448 If this is greater than 0 for all real x, the discriminant must be < 0
This will guarantee that the graph will always be above the x axis
So
[ 2(4k - 1)]^2 - ( 4) ( 15k^2 - 2k - 7) < 0 simplify
4 [ 16k^2 - 8k + 1 ] - 60k^2 + 8k + 28 < 0
64k^2 - 32k + 4 - 60k^2 + 8k + 28 < 0
4k^2 - 24k + 32 < 0 divide through by 4
k^2 -6k + 8 < 0
( k - 4)(k - 2) < 0
This will be true when 2 < k < 4
